We prove an extension of Hardy’s classical characterization of real Gaussians of the form e−παx 2 , α > 0 to the case of complex Gaussians in which α is a complex number with positive real part. Such functions represent rotations in the complex plane of real Gaussians. A condition on the rate of decay of analytic extensions of a function f and its Fourier transform f̂ along some pair of lines in...

Contour information is an important source for object perception and memory. Three experiments examined the precision of visual short-term memory for complex contour shapes. All used a new procedure that assessed recall memory for holistic information in complex contour shapes: Participants studied, then reproduced (without cues), a contoured shape by freehand drawing. In Experiment 1 memory pr...

The ambiguity involved in reconstructing an image from limited Fourier data is removed using a new technique that incorporates prior knowledge of the location of regions containing small-scale features of interest. The prior discrete Fourier transform (PDFT) method for image reconstruction incorporates prior knowledge of the support, and perhaps general shape, of the object function being recon...

A generic Fourier-space approach to solve the self-consistent field theory of block copolymers is developed. This approach is based on the fact that, for any computational box with periodic boundary conditions, all spatially varying functions are spanned by the Fourier series determined by the size and shape of the box. The method reproduces all known diblock copolymer phases. The application o...

New microscope technologies are enabling the acquisition of large volumes of live cell image data. Accurate temporal object tracking is required to facilitate the analysis of this data. One principal component of cell tracking is correspondence, matching cells between consecutive frames. This component can be enhanced by incorporating shape metrics into the tracking model. The measure of shape ...

By exploiting the analyticity and boundary value properties of the thermal Green functions that result from the KMS condition in both time and energy complex variables, we treat the general (non–perturbative) problem of recovering the thermal functions at real times from the corresponding functions at imaginary times, introduced as primary objects in the Matsubara formalism. The key property on...

Fourier spectrum of the boundary values of functions in the complex Hardy Space H(C+) is characterized for p ∈ (0, 2). First, functions f in the L(R) can be decomposed into a sum g + h, where g and h are the non-tangential boundary limits of function in H(C+) and H(C−) in the sense of L(R), where H(C+) and H(C−) are the Hardy spaces in the upper and lower complex plane C+ and C−, respectively. ...

A reverse of the Cauchy-Bunyakovsky-Schwarz integral inequality for complex-valued functions and applications for the finite Fourier transform are given.